Most machines designed to recognize forms (such as printed character analyzers), represent the image (e.g. a printed or typed character) by a two dimensional array of numbers in electronic form. The numbers usually represent the brightness and/or color levels in the image.
The shape or pattern contained in the array is then analyzed by one of several methods. Most often elaborate "segmentation" procedures are used. These break the shape or pattern into its component "features," which are analyzed individually and then collectively. (For example, see U.S. Pat. No. 4,115,761 to Ueda et al. (1978), and Image Analysis: Problems, Progress and Prospects, A. Rosenfeld, 17, Pattern Recognition 3-12 (1984) for a review.)
Alternatively, the shape properties of the array may be evaluated by using the information contained in the rows, columns, and diagonals (called the "cross sections") of the array. The information collected along each cross section is encoded for certain characteristics, and this analysis is combined with the summaries from other cross sections. This provides information which the machine uses to classify the pattern or shape contained by the image, or for comparison among the images being analyzed. For examples of this approach, see U.S. Pat. Nos. 3,860,909 to Demonte (1975) and 4,398,177 to Bernhardt (1983).
Each of the previous methods has its disadvantages. The method of Ueda et al. (op. cit.) requires an exhaustive study of the subject matter before the machine can be designed. The basic component shapes or "features" must be selected beforehand, and a single machine cannot be adapted to a variety of recognition tasks. The method of Bernhardt (op. cit.) requires that the location of the cross section be retained as part of the summary information. Storing this location puts a burden on the memory of the system, and analysis is not feasible if the camera and object are in relative motion.
An analysis method described by E. Wong & J. Steppe (Invariant Recognition of Geometric Shapes, in S. Watanabe, Methodologies of Pattern Recognition, Academic Press: N.Y., 1969, pp. 535-546), eliminates the requirement to store location of the cross section, and is not sensitive to relative motion between the camera and its object. These authors suggest that the shape properties can be summarized by a frequency distribution of chord lengths. Chord lengths, taken at various angles, are measured from edge to edge across the form, and the frequency of observed length is plotted as the dependent variable with all possible lengths being the independent variable. However, they consider only nondiscrete sampling of the image form, using a (theoretically) infinite number of "scan lines" or "scan angles," and measuring a continuum of possible lengths along each line. This is impractical for machine purposes. Additionally, the "chord length" measure provides a summary which is not useful in the analyis of complex forms.
Most importantly, previous methods of cross sectional analysis have provided arbitrary or overly limited definitions of what constitutes the information contained by the cross section. Thus far, none have provided a comprehensive and flexible criterion for extracting information from complex patterns and shapes, and providing for classification and comparison of the images as would be needed for effective machine vision.